That sounds like a good approach. Just remember to read all the upgrade notes between your current version and the one you'll be upgrading to.
The only thing that needs to change is that you checkout a version after the clone.
git clone https://github.com/getodk/central
git checkout v2023.1.0
git submodule update -i
...
The rest of the commands should work, but when you need to upgrade in the future, you'll need to remember to git checkout master first and deal with whatever merge conflicts exists.